[R-sig-ME] Calculating fixed effect contrasts with log-transformed data

[Gus Jespersen]

Greetings,
I doubt this is a particularly interesting question for you mixed
model gurus, but here goes.  As you can see in the output below, I
have a model with twelve fixed effect parameters.  I am interested in
each of the "Treatment" vs. "Control" comparisons for each "site"(in
each fixed effect parameter name, these are specified by the text
immediately following "sitett"). To produce a 95% CI for such a
comparison I was advised to take two steps:

(1) Subtract the Control parameter estimate from the Treatment
parameter estimate for each site.
(2) Compute the SE for this comparison via:  sqrt( var(treatment) +
var(control) - 2*cov(treatmentt,control)).  To get these values I am
using the vcov matrix for the model.

When I move to log10-transformed data, I am thinking I should
backtransform the fixed effects and SE's before moving ahead  with the
Control-Treatment comparisons.  However, the calculations become more
problematic as ( var(treatment) + var(control) -
2*cov(treatmentt,control)) is consistently negative.  I am uncertain
on how to proceed here.  Any advice would be much appreciated.

Thank you,
Gus

Data: data.file.final
Models:
Mod.NO3.1.2: NO3Nyearone ~ 1 + (1 | pr)
Mod.NO3.1.1: NO3Nyearone ~ 1 + sitett + (1 | pr)
            Df    AIC    BIC  logLik  Chisq Chi Df Pr(>Chisq)
Mod.NO3.1.2  3 1163.5 1172.2 -578.72
Mod.NO3.1.1 14 1155.8 1196.7 -563.90 29.637     11   0.001806 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Linear mixed model fit by REML
Formula: NO3Nyearone ~ 1 + sitett + (1 | pr)
   Data: data.file.final
  AIC  BIC logLik deviance REMLdev
 1098 1139 -534.8     1128    1070
Random effects:
 Groups   Name        Variance Std.Dev.
 pr       (Intercept)  33.348   5.7747
 Residual             210.115  14.4954
Number of obs: 137, groups: pr, 72

Fixed effects:
                             Estimate Std. Error t value
(Intercept)                    20.118      4.701   4.280
sitettLepAddition Treatment     3.032      6.069   0.500
sitettMossAddition Control      5.677      6.809   0.834
sitettMossAddition Treatment    9.418      6.648   1.417
sitettMossRemoval Control      -9.951      6.510  -1.529
sitettMossRemoval Treatment    -9.601      6.510  -1.475
sitettSaddle Control          -10.985      6.510  -1.687
sitettSaddle Treatment        -12.269      6.648  -1.846
sitettToeAdditions Control      0.932      6.510   0.143
sitettToeAdditions Treatment  -11.678      6.809  -1.715
sitettToeRemoval Control      -12.351      6.510  -1.897
sitettToeRemoval Treatment    -13.168      6.510  -2.023



-- 
R. Gus Jespersen
PhD Candidate
College of Forest Resources
University of Washington
Box 352100
Seattle, WA 98195-2100
(206) 543-5777
jesper at u.washington.edu